Question

1- Explain how you would test the hypotheses for paired difference between the means of two populations. Give an example.

2- Explain how the proportions for two populations are used in hypotheses testing about two population proportions. Give an example.

Note: type it if possible.

Answer 1

1)

If we want to test if the proportion of one child homes in Florida is larger than the proportion of one child homes the state of Florida. Alabama

Two independent studies were conducted,

89 out of 350 homes in Alabama had one child, and

152 out of 400 had one child in Florida.

Is there sufficient evidence the proportion of one child homes in Florida is greater than in Alabama ?

p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ > 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	152	400	89	350	0.12571429	0.034180055	3.6780012	0.0001

since p-value < 0.0001

we reject the null hypothesis

we conclude that there is evidence that proportion of one child homes in Florida is greater than in Alabama